%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS105+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:23 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS105+1 : TPTP v9.0.0. Released v3.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:11:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(ra_Px1_type, type, (
% 0.20/0.37 ra_Px1: ( $i * $i ) > $o)).
% 0.20/0.37 tff(i2003_11_14_17_20_53634_type, type, (
% 0.20/0.37 i2003_11_14_17_20_53634: $i)).
% 0.20/0.37 tff(cd_type, type, (
% 0.20/0.37 cd: $i > $o)).
% 0.20/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.37 tptp_fun_Y_0: $i > $i)).
% 0.20/0.37 tff(ca_Ax2_type, type, (
% 0.20/0.37 ca_Ax2: $i > $o)).
% 0.20/0.37 tff(rr_type, type, (
% 0.20/0.37 rr: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.37 tptp_fun_Y_2: $i > $i)).
% 0.20/0.37 tff(cc_type, type, (
% 0.20/0.37 cc: $i > $o)).
% 0.20/0.37 tff(cUnsatisfiable_type, type, (
% 0.20/0.37 cUnsatisfiable: $i > $o)).
% 0.20/0.37 tff(tptp_fun_Y0_1_type, type, (
% 0.20/0.37 tptp_fun_Y0_1: $i > $i)).
% 0.20/0.37 tff(cdxcomp_type, type, (
% 0.20/0.37 cdxcomp: $i > $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (^[X: $i] : rewrite((~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))) <=> (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))) <=> ![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (^[X: $i] : refl((~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))) <=> (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))) <=> ![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (^[X: $i] : rewrite((~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))) <=> (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))) <=> ![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))) <=> ![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))) <=> (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))), (((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))) <=> ((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))), rewrite(((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))) <=> (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))), (((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))) <=> (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (![X: $i] : ((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))) <=> ![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (^[X: $i] : rewrite(((ra_Px1(X, tptp_fun_Y_0(X)) | cd(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))) <=> ((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (![X: $i] : ((ra_Px1(X, tptp_fun_Y_0(X)) | cd(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X)))) <=> ![X: $i] : ((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px1(X, Y)) <=> (~?[Y: $i] : ra_Px1(X, Y))), ((cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y))))), rewrite((cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X)))), ((cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X))))), rewrite((~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X)))), ((cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (![X: $i] : (cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.37 tff(15,axiom,(![X: $i] : (cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cd(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.37 tff(18,plain,(
% 0.20/0.37 ![X: $i] : ((ra_Px1(X, tptp_fun_Y_0(X)) | cd(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[17])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (![X: $i] : ((cd(X) | ra_Px1(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cd(X))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((~![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))) | (~((~(cd(i2003_11_14_17_20_53634) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y_0(i2003_11_14_17_20_53634)))) | (~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (~((~(cd(i2003_11_14_17_20_53634) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y_0(i2003_11_14_17_20_53634)))) | (~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (((~(cd(i2003_11_14_17_20_53634) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y_0(i2003_11_14_17_20_53634)))) | (~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))))) | ((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 ((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.37 tff(27,assumption,(~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))), introduced(assumption)).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 ((cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))) | rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 ((cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))) | (~cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (~cc(tptp_fun_Y_2(i2003_11_14_17_20_53634))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (cUnsatisfiable(i2003_11_14_17_20_53634) <=> cUnsatisfiable(i2003_11_14_17_20_53634)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(33,axiom,(cUnsatisfiable(i2003_11_14_17_20_53634)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_9')).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (cUnsatisfiable(i2003_11_14_17_20_53634)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (^[X: $i] : refl((cc(X) | (~cUnsatisfiable(X))) <=> (cc(X) | (~cUnsatisfiable(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X: $i] : (cc(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![X: $i] : (cc(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (^[X: $i] : rewrite((cUnsatisfiable(X) => cc(X)) <=> (cc(X) | (~cUnsatisfiable(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![X: $i] : (cUnsatisfiable(X) => cc(X)) <=> ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.38 tff(40,axiom,(![X: $i] : (cUnsatisfiable(X) => cc(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.38 tff(43,plain,(
% 0.20/0.38 ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[42])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | (cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))) <=> ((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | (cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 ((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (cc(i2003_11_14_17_20_53634)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (^[X: $i] : refl(((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (^[X: $i] : rewrite(((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(52,plain,
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% 0.20/0.38 inference(quant_intro,[status(thm)],[51])).
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% 0.20/0.38 inference(bind,[status(th)],[])).
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% 0.20/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.38 tff(57,axiom,(![X: $i] : (cc(X) => ![Y: $i] : (rr(X, Y) => cc(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
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% 0.20/0.38 inference(bind,[status(th)],[])).
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% 0.20/0.38 inference(quant_intro,[status(thm)],[71])).
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% 0.20/0.38 inference(bind,[status(th)],[])).
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% 0.20/0.38 inference(quant_intro,[status(thm)],[73])).
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% 0.20/0.38 (((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | (cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634)))) <=> ((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(105,plain,
% 0.20/0.38 ((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | (cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(106,plain,
% 0.20/0.38 ((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.38 tff(107,plain,
% 0.20/0.38 (cd(i2003_11_14_17_20_53634)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[106, 103, 93])).
% 0.20/0.38 tff(108,plain,
% 0.20/0.38 ((~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))) | (~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(109,plain,
% 0.20/0.38 ((~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.38 tff(110,plain,
% 0.20/0.38 (![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[109, 26])).
% 0.20/0.38 tff(111,plain,
% 0.20/0.38 (^[X: $i] : refl((~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(112,plain,
% 0.20/0.38 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.38 tff(113,plain,
% 0.20/0.38 (^[X: $i] : rewrite((~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(114,plain,
% 0.20/0.38 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.38 tff(115,plain,
% 0.20/0.38 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.38 tff(116,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))) <=> (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))), ((((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))), rewrite((((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))), ((((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(117,plain,
% 0.20/0.38 (![X: $i] : (((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.38 tff(118,plain,
% 0.20/0.38 (![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0)) <=> ![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(119,axiom,(![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.38 tff(120,plain,
% 0.20/0.38 (![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.38 tff(121,plain,(
% 0.20/0.38 ![X: $i] : (((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[120])).
% 0.20/0.38 tff(122,plain,
% 0.20/0.38 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.20/0.38 tff(123,plain,
% 0.20/0.38 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.20/0.38 tff(124,plain,
% 0.20/0.38 ((~![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))) | (~((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | (~(cdxcomp(i2003_11_14_17_20_53634) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y0))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (~((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | (~(cdxcomp(i2003_11_14_17_20_53634) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y0)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.39 tff(126,plain,
% 0.20/0.39 (((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | (~(cdxcomp(i2003_11_14_17_20_53634) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y0))))) | ((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(127,plain,
% 0.20/0.39 ((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 (^[X: $i] : refl((cdxcomp(X) | (~cUnsatisfiable(X))) <=> (cdxcomp(X) | (~cUnsatisfiable(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(129,plain,
% 0.20/0.39 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.39 tff(130,plain,
% 0.20/0.39 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(131,plain,
% 0.20/0.39 (^[X: $i] : rewrite((cUnsatisfiable(X) => cdxcomp(X)) <=> (cdxcomp(X) | (~cUnsatisfiable(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(132,plain,
% 0.20/0.39 (![X: $i] : (cUnsatisfiable(X) => cdxcomp(X)) <=> ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.39 tff(133,axiom,(![X: $i] : (cUnsatisfiable(X) => cdxcomp(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.39 tff(134,plain,
% 0.20/0.39 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.39 tff(135,plain,
% 0.20/0.39 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.20/0.39 tff(136,plain,(
% 0.20/0.39 ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[135])).
% 0.20/0.39 tff(137,plain,
% 0.20/0.39 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.20/0.39 tff(138,plain,
% 0.20/0.39 (((~![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))) | (cdxcomp(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))) <=> ((~![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))) | cdxcomp(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(139,plain,
% 0.20/0.39 ((~![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))) | (cdxcomp(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(140,plain,
% 0.20/0.39 ((~![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))) | cdxcomp(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.39 tff(141,plain,
% 0.20/0.39 (cdxcomp(i2003_11_14_17_20_53634)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[140, 137, 34])).
% 0.20/0.39 tff(142,plain,
% 0.20/0.39 ((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | (~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(143,plain,
% 0.20/0.39 ((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.20/0.39 tff(144,plain,
% 0.20/0.39 (ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[143, 127])).
% 0.20/0.39 tff(145,plain,
% 0.20/0.39 ((~![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))) | (~ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(146,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[145, 144, 110])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------